Precalculus Examples

$\log (\sqrt{b^{7} c})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b^{7} c}$ as ${(b^{7} c)}^{\frac{1}{2}}$ .

$\log ({(b^{7} c)}^{\frac{1}{2}})$

Step 2

Expand $\log ({(b^{7} c)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (b^{7} c)$

Step 3

Rewrite $\log (b^{7} c)$ as $\log (b^{7}) + \log (c)$ .

$\frac{1}{2} (\log (b^{7}) + \log (c))$

Step 4

Expand $\log (b^{7})$ by moving $7$ outside the logarithm.

$\frac{1}{2} (7 \log (b) + \log (c))$

Step 5

Apply the distributive property.

$\frac{1}{2} (7 \log (b)) + \frac{1}{2} \log (c)$

Step 6

Multiply $\frac{1}{2} (7 \log (b))$ .

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Step 6.1

Combine $7$ and $\frac{1}{2}$ .

$\frac{7}{2} \log (b) + \frac{1}{2} \log (c)$

Step 6.2

Combine $\frac{7}{2}$ and $\log (b)$ .

$\frac{7 \log (b)}{2} + \frac{1}{2} \log (c)$

Step 7

Combine $\frac{1}{2}$ and $\log (c)$ .

$\frac{7 \log (b)}{2} + \frac{\log (c)}{2}$